We've all heard the mild joke that a monkey, throwing darts at the financial pages, can pick stocks as well as a professional. In no small part it was this mental image that motivated the index fund industry. Lately a new claim is current: A cat's stock picks can beat the S&P 500 index.

There are have been a couple of stock-picking cats. Last year the Observer invited three financial pros to compete against a ginger cat named Orlando and a group of British students. The cat's random picks (made by having the cat throw a toy mouse at a marked grid of stocks) outperformed the portfolios of the pros and the kids.

Bob, another stock-picking cat, watching a human friend on TV

In the U.S., the best-known stock-picking cat is the recently deceased Bob, owned by PIMCO bond guru William H. Gross. Wrote Gross: "I often asked her [Bob was female] about her recommendations for pet food stocks, and she frequently responded—one meow for 'no,' two meows for a 'you bet.'"

It will be apparent that cats are replacing monkeys as the favored metaphor for "random" stock picking. (Cat people are free to find this demeaning.) In any case, hedge fund manager David Harding, of Winton Capital, recently weighed in on the matter on CNBC. He didn't mention cats, but he described a system of picking 50 stock "at random" and weighting them equally. "We tested the idea and [it] immediately did better than the S&P 500."

Harding says he's raised $1 billion to invest in this random-50-stocks scheme, and it's been outperforming the market.

Is it possible that random picks (a "cat") can consistently outperform a broad market index like the S&P 500? It is. But let me first point out that that Observer contest doesn't mean much. It tracked the three portfolios over a year. Obviously there's a strong element of luck in that time frame. Suppose you and I competed at the roulette table. After a night of gambling one of us will do better than the other, but it would be wrong to conclude that the winner has superior skill. Roulette is dumb luck, and in the short term, the stock market is very close to that.

Note that the Observer folks stacked the deck in favor of getting a click-friendly "man bites dog" headline. There was a two-third chance that either the cat or the school kids would beat the pros.

The S&P index tracks the 500 largest American stocks. Its purpose is to gauge the market performance of the companies most popular with investors and most important to the American economy. The S&P index was never intended to set a cap on what returns investors may expect in a close-to-efficient market.

The S&P index is market weighted. It does not, in other words, track the worth of a portfolio invested equally in all 500 included stocks. Instead it assume the portfolio is weighted according to market capitalization. Apple, for instance, has recently been over 4 percent of the index (not 1/500 or 0.2 percent).

This means that every S&P index fund is strongly overweighted in Apple (and other big, popular companies like Exxon Mobil, Microsoft, and IBM). What's wrong with that? As Harding explains:

"If you have the same expected returns from assets you should put the same weights on them to optimize the portfolio. So if you choose stocks at random and combine them, you will always beat S&P 500, or in 99.99 percent of cases."

Anyone who truly believes that all 500 S&P companies have equally good expected returns—as an efficient market theory diehard might—would want to invest equally in all. You should put 1/500 of your portfolio in each. By overweighting a few popular companies, you take on extra risk without getting anything in return.

Now maybe you don't believe the market is all efficient, all the time. I don't, either. Unfortunately, there is little reason to believe that popular stocks merit their popularity. The evidence is that big and popular companies do worse than small and obscure ones.

The most popular stock of the moment is likely to be overbid. It won't always be most popular. Apple is such a market darling right now that it's hard to believe that posterity will look back and marvel at how undervalued it was in 2014. That means Apple's long-term return expectations are likely to be less than average for S&P 500 stocks.

For that reason, a balanced portfolio of all 500 S&P stocks, each comprising 1/500 of total assets, might be expected to have slightly better return and slightly lower volatility than the official S&P 500 index or funds tracking it.

You can do better than that. It is well established that stocks of small companies have outperformed those of large companies over long periods. A "random" basket of stocks, not restricted to the 500 largest, thus might be expected to outperform the S&P index—assuming the small cap bias persists in the future.

For that reason I find Harding's claim easy to believe. Investing in 50 random stocks is marvelously simple. The one thing I don't get: why would sophisticated investors pay hedge fund fees (assuming they are) for a system they could duplicate themselves? (Then again, Harding's fund may have a few twists he's not talking about on CNBC.)